Decoupling, exponential sums and the Riemann zeta function

@article{Bourgain2014DecouplingES,
  title={Decoupling, exponential sums and the Riemann zeta function},
  author={Jean Bourgain},
  journal={Journal of the American Mathematical Society},
  year={2014},
  volume={30},
  pages={205-224}
}
  • J. Bourgain
  • Published 25 August 2014
  • Mathematics
  • Journal of the American Mathematical Society
We establish a new decoupling inequality for curves in the spirit of [B-D1], [B-D2] which implies a new mean value theorem for certain exponential sums crucial to the Bombieri-Iwaniec method as developed further in [H]. In particular, this leads to an improved bound $|\zeta(\frac 12+it)|\ll t^{53/342+\varepsilon}$ for the zeta function on the critical line 
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On the order of ζ ( 12 + it )
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